Vectors in the Plane

  1. \rhd Introduction to vectors and scalars (8:38) A discussion on vectors and scalars.
  2. \rhd Recognizing vectors (2:35) Which of the following can represent a vector? Select all that apply.
    1. The number 5
    2. The angle measure 5^{\circ}
    3. The point (5,5)
    4. The outcome of 5+5
  3. * Practice: Recognizing vectors. (2 problems)
  4. \rhd Equivalent vectors (6:36) When are two vectors equivalent.
  5. * Practice: Equivalent vectors. (4 problems)
  6. \rhd Finding the magnitude (3:05) The magnitude of \vec{a}= \langle 5,-3\rangle.
  7. \rhd Scalar multiplication of vectors (5:41) Given that \vec{w}= \langle 1,2\rangle, find 3\vec{w} and -2\vec{w}. What do they represent geometrically?
  8. * Practice: Scalar multiplication. (4 problems)
  9. \rhd Adding and subtracting vectors (7:41) Given that \vec{a}= \langle 3,-1\rangle and \vec{b}= \langle 2,3\rangle, what are \vec{a}+\vec{b} and \vec{a}-\vec{b}?  What do they represent geometrically?
  10. \rhd Combined vector operations (5:58) Given that \vec{u}= \langle 2,-1\rangle and \vec{w}= \langle -5,5\rangle, what are 3\vec{u}+\dfrac{1}{5}\vec{w} and \vec{a}-\vec{b}? What does it represent geometrically?
  11. * Practice: Combined vector operations. (4 problems)
  12. \rhd Finding unit vector with given direction (5:01) Find a unit vector in the direction of \vec{a}= \langle 3,4\rangle.
  13. * Practice: Unit vectors. (4 problems)
  14. \rhd Direction of a vector (1st and 2nd quadrant) (9:00) Find the directions of \vec{u}= \langle 3,4\rangle and \vec{w}= \langle -5,6\rangle.
  15. \rhd Direction of a vector (3rd and 4th quadrant) (6:41) Find the directions of \vec{a}= \langle -2,-4\rangle and \vec{b}= \langle 4,-6\rangle.
  16. * Practice: Direction of vectors. (4 problems)